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Harold Edwards published his book Essays in Constructive Mathematics in 2005 but continued to think deeply about the themes discussed in the essays. At the time of his death in November 2020, Edwards was completing a long essay that contained his final thoughts on three of his favorite topics: Galois’s first memoir, points on an algebraic curve, and Abel’s theorem.
The literary form of the essay goes back to Michel de Montaigne, whose Essais were first published in 1580. The 1588 edition added new essays, and the 1595 posthumous edition was heavily revised. In other words, Montaigne’s Essais were not static—they evolved and grew in scope as his thoughts developed over the years. The same is true for Professor Edwards and how he thought about his Essays.
This new edition of the Essays consists of two parts. Part I contains of the original Essays from 2005 with typographical corrections. Part II is based primarily on Edwards’s final manuscript, with additions that supply missing details and enhance the connection to the essays in Part I. However, the two parts are largely independent of each other, so either part can be read without having to worry about the other. The Postscript describes the changes and additions made to Edwards’s manuscript.
Part I consists of Chapters 1–5, each divided into sections that are the essays. Part II has a similar structure, with Chapters 6–9 also divided into essays. Thus, “Essay 2.3” means the third essay of Chapter 2.
More details about the precise contents of Parts I and II can be found in the synopses of each part. The reader should also consult the preface of each part to hear Edwards’s unique voice as he introduces the mathematics to follow